The electromagnetic spectrum is divided into frequency bands. For example, the W-band of the electromagnetic spectrum ranges from 75 to 110 GHz. It resides above the V-band (50-75 GHz) in frequency, yet overlaps the NATO designated M-band (60-100 GHz). The W-band is used for radar research, military radar targeting and tracking applications, as well as for non-military applications such as automotive radar receivers.
Unfortunately, the power gain of integrated circuits designed to work in these frequency bands is subject to considerable variations due to changes of the ambient temperature either caused by the application itself or by changing temperature conditions of the surrounding atmosphere or neighboring devices.
As an example, FIG. 1 schematically shows a chip block diagram of a 77 GHz car radar receiver 100, which consists of 4 main building blocks: a low noise amplifier (LNA) 102 with a control input 104 and a signal input 122, a fully differential Gilbert mixer with passive balun 106 and terminals 108 for applying frequency adjustment capacitance, a baseband intermediate frequency buffer 110 with output terminals 112 providing an intermediate frequency signal, and a doubler block 114 with a doubler 116 and a 38 GHz buffer amplifier 118 with local oscillator input/output terminals 120. The LNA may be implemented based on Silicon Germanium (SiGe) bipolar technology. Here the power gain of the LNA might vary considerably with temperature. It can be expected that the gain decreases by about as much as 10 dB with a temperature increasing from −40° C. to +125° C. At the same time, the noise performance of the LNA decreases with rising temperature, i.e. the noise figure NFLNA of the LNA increases. As it can be seen from eq. 1, the total noise figure of the whole system increases with increasing NFLNA. Furthermore, NFtotal mainly depends on NFLNA for high LNA gains GLNA (typically more than 10 dB).
Total system noise figure:
                              NF          total                =                              NF            LNA                    +                                                    NF                mixer                            -              1                                      G              LNA                                +                                                    NF                Baseband                            -              1                                                      G                LNA                            ⁢                              G                mixer                                                                        (                  eq          .                                          ⁢          1                )            
In which Gmixer represents the gain of the mixer, NFmixer the noise figure of the mixer and NFbaseband the noise figure of the baseband components.
The low noise amplifier 102 shown in FIG. 1 is the first active stage of the receiver 100 and determines the overall system performance. In order to achieve sufficient gain of the LNA, two common emitter cascode stages with one buffer stage are cascaded. FIG. 2 shows a schematic diagram of a cascode circuit 200 based on SiGe HBT (heterojunction bipolar transistors) 202, 204, with matching networks at the transistor input and output, realized by microstrip transmission lines 206-218 used to convey the microwave-frequency signals plus capacitors and resistors 220-232 for DC decoupling and low pass filtering. The circuit comprises inputs for a received signal 234, supply voltages VCAS 238 and VCC 240 and for an additional bias voltage VB1 242 and output 236 to the next stage.
In car radar receiver systems as shown in FIG. 1, the temperature dependence of the total conversion gain is an important factor. Since phase and amplitude information of the intermediate frequency IF-signal can be used to detect objects (car, walls, pedestrians), a receiver with temperature dependent gain that spoils detection results is a disadvantage.
In order to avoid wide amplitude variations in the output signal leading to a loss of information or to an unacceptable performance of the system, AGC (automatic gain control) circuits are usually employed in baseband to control the output signal, if the gain variation is considerably large.
W-band LNAs can be designed based on SiGe bipolar technology, e.g. a 0.18 μm SiGe technology, providing cutoff frequencies fmax/fT about 290/200 GHz at room temperature. But temperature dependent variation of fT and fmax is quite large for such a device. Hence, the power gain of such an LNA varies considerably with respect to temperature.
In order to obtain a low variation of gain and system noise figure within the mentioned wide temperature range a car radar system has to deal with, bias voltages for both cascode stages and output buffer stage can be applied, as shown in FIG. 2 for a cascode stage. An optimized relationship between ambient temperature and these bias voltages can be derived. An optimized solution can be obtained, for example, by applying the noise measure method (a compromise between gain and noise), as mentioned in “A 77 GHz (W-band) SiGe LNA with a 6.2 dB Noise figure and Gain Adjustable to 33 dB”, Reuter, R., Yin Y., IEEE Bipolar/BiCMOS Circuits and Technology Meeting, 7.2, October 2006, pp: 1-4. An example of desired optimized bias voltages for the first and second stage VB1 (310) and output buffer stage VB2 (312) are illustrated in FIG. 3. Both voltages show a linear dependence over temperature and a small negative temperature coefficient in the range of −0.42 mV/° C. and −0.67 mV/° C., respectively.
In order to apply voltages that approximate these desired bias voltages 310, 312, allowing for optimized temperature compensation, a DC voltage reference may be established with a temperature behavior suitable for compensating the temperature behavior of the LNA circuit. In state-of-the-art LNA designs, as described in “A 1-GHz BiCMOS RF Front-End IC”, R. Meyer and W. Mack, IEEE Journal of Solid State circuit, vol. 29, No. 3, pp. 350-355, March 1994, the proportional-to-absolute-temperature (PTAT) compensation principle is commonly used (R. J. Widlar, Low voltages techniques, IEEE Journal of Solid-State Circuits, 13(6):836-846, December 1978). A schematic diagram of a basic PTAT compensation circuit 400 is shown in FIG. 4. A PTAT current is generated by using the difference in forward voltage appearing across a resistor when two diode-connected transistors (402 and 404) are operated at different current densities. This results in a difference voltage generating a PTAT current in resistor 406. The PTAT current is mirrored into transistor 408 and resistor 410, and by adjusting resistor 410 to the correct multiple K of resistor 406 the desired VREF over temperature can be achieved, where the forward voltage of diode-connected transistor 408 is the inverse of PTAT, or complementary-to-absolute-temperature (CTAT), and the CTAT of base-emitter voltage VBE of transistor 408 and PTAT voltages are compensated. PMOS-transistors 412-416 are used for current supply and mirroring, operational amplifier 418 adjusts the gate voltage of the PMOS devices 412-416 so as to equalize the voltage levels at its positive and negative input terminals. The basic PTAT compensation principle is shown in FIG. 5. A temperature dependent PTAT voltage is provided and compensated with a CTAT voltage with negative temperature coefficient, resulting in a linear compensated reference voltage. In FIG. 5 the basic PTAT principle is shown. Since generally in semiconductors, the relationship between the flow of electrical current and the electrostatic potential across a p-n junction depends on a characteristic voltage called the thermal voltage, it is denoted VT=kT/q, where q is the magnitude of the electrical charge (in coulombs) on the electron, and k the Boltzmann constant. In FIG. 4, a PTAT voltage VT is the temperature dependent VBE voltage of transistor 402, whereas a CTAT VBE voltage in FIG. 5 relates to VBE voltage of transistor 408.
However, it is well known that the base-emitter voltage VBE of a diode-connected bipolar transistor comprises a non-linear term (cf. Varshni, Y. P., “Temperature dependence of the energy gap in semiconductors”, Physica, 1967, 34, pp. 149-154):VBE=Vgo+αT+f(T2)  (eq. 2)
Vgo is the silicon band-gap voltage at zero Kelvin; α depends on the current density of the diode-connected bipolar transistor; f (T2) represents the second-order nonlinearities in the base-emitter voltage. Thus, with the state-of-the-art PTAT compensation method and circuit illustrated in FIG. 4 higher order dependencies cannot be cancelled. Practically, when a plot of the reference voltage VREF (T) provided by the PTAT compensation circuit against temperature T is expected to have a rather small slope, the second-order non-linearity will play a significant role, as shown in FIG. 6, hence an approximation of the desired linear relationship between bias voltage and temperature is difficult.
U.S. Pat. No. 6,118,264 discloses a complex approach to producing a voltage reference having a temperature compensation on second order events by providing a band-gap reference voltage circuit based on a Brokaw cell for producing a band-gap voltage reference and a compensation voltage approximating the band-gap voltage over temperature, wherein the sum of both voltages partly reduces the influence of second order events.
U.S. Pat. No. 5,129,049 discloses a temperature compensated reference voltage generation circuit that uses different current sources, one with increasing current, another one with decreasing current as temperature increases, for approximation of a voltage change across a resistor with respect to temperature.